What is the difference between a clean style and powerlifting style deadlift?

There is no such distinction. There never was. I am sure that many powerlifters think that they have a style of deadlifting that should be called a "powerlifting style deadlift" but the deadlift is not a derivative of the clean and jerk and there is no style that distinguishes such.

What makes a "pull" slow or fast. Is it a choice? After all we can do speed deadlifts. So does that make the deadlift a fast pull?

These questions come up because most strength trainees have been trained in the slow lifts but not the fast Olympic lifts. The information they have received about the fast lifts is from those who "dabble" in them. Alternatively they receive information from those who only dabble in strength in general…but that is another subject.

Somebody recently implied that I try to sell pure strength training to everybody. The idea being, I suppose, that I want to convince everybody to engage in maximum strength training and think it is "bad" if they don't, or, by extension, fail to follow my advice. Well, those who have read my blog extensively, of course, know better, since the "selling of strength" training is something I adamantly oppose and often complain about.